South Carolina Sen. Lindsey Graham told reporters on Capitol Hill on Tuesday, leaving a meeting of the Republican conference, that he now believes only a one- or two-year extension of the DACA program, which protects young undocumented immigrants who came to the US as children, is likely.

The dire prediction came from a longtime advocate of immigration reform who has been one of the strongest supporters of getting a permanent solution to DACA -- and who had a confrontation with President Donald Trump about vulgar comments the President made in rejecting a bipartisan compromise Graham negotiated.

"I'm becoming increasingly pessimistic about immigration," Graham said. "I don't think we're going to do a whole lot beyond something like the BRIDGE Act, which would be extend DACA for a year or two, and some border security. It's just too many moving parts."

Graham's comments came before said on Tuesday he supports a government shutdown if Democrats won't agree to tighten immigration laws, undercutting ongoing bipartisan negotiations on Capitol Hill.

Graham, who has also been a part of bipartisan Senate meetings that are seeking a compromise and who helped convince Senate Majority Leader Mitch McConnell to promise to bring immigration to the floor in a "fair" process next week, called that option unsatisfactory but likely.

"That will be a punt, that will not be winning for the country, but that's most likely where we're going to go," Graham said.

He alsotook a jab at some colleagues who have said that any deal must be done in stages to avoid comprehensive immigration reform, a common refrain from Republicans across the spectrum.

"Comprehensive is hard -- the only thing harder than comprehensive is doing it in smaller steps," Graham said. "So, all those who criticize comprehensive immigration, saying we should do it in smaller stages: This is what you run into."

Graham also said that while he supports much of what the White House has proposed -- pieces of the offer like substantially cutting family-based migration, or what some Republicans call "chain migration," and ending the diversity lottery are a tough sell without legalizing all 11 million undocumented immigrants in the US. He also accused some of his Democratic colleagues of having "unreasonable" demands.

Graham's comments were backed up by his close ally on immigration, Arizona Republican Sen. Jeff Flake, who said private meetings on Monday also left him pessimistic that a deal could be reached.

"Yesterday, yeah, we took a few steps back I think," Flake said when asked by CNN about Graham's prediction. "Just people insisting that we include too much."

Flake said in "a few of the meetings" there was support for putting a bill like the White House proposal on the floor for a vote -- which Flake said likely couldn't get 60 votes to advance. Flake said he only believes a DACA and border security deal can pass.

"If you start adding in all the other things, it's going to be too big," Flake said. But he added: "I don't know, you're pessimistic one day, optimistic the next. Yesterday we were pessimistic, hopefully today we'll feel differently."

The impasse leaves Graham believing a pathway to citizenship for DACA recipients can't pass Congress because the White House wants more on that than the Senate can give.

"You're not going to give a pathway to citizenship unless you give the things the President wants. ... The chain migration and the visa lottery are going to are the problem areas," Graham said. He added he wasn't telling the White House to back off, necessarily, but that the "likelihood" of that getting enough votes to advance legislation in the Senate on that is "pretty small."

"I think it would be a huge mistake to just have a short-term extension of the DACA program because then we're just going to be fighting the same old battles when it expires ... and it keeps the cloud of doubt and fear over the DACA young adults, and I don't think that's a good situation," Collins said. "We have all the ability in the world to come up with a solution. I think the Senate ought to legislate in that area.".